How a gyroscope works

I have searched through many texts. But I have never found an explanation of
why a gyroscope should resist being turned in any direction perpendicular to
it's axis. Maybe the workings of a gyroscope seem obvious to some and needs no
explanation. But still, other obvious physical phenomena are explained. So here
is the first published (that I know of) account of the physics behind how a
gyroscope works.

Here is a pictorial of a simplified version of a gyro.

Instead of a complete rim, four point masses, A, B, C, D, represent the areas
of the rim that are most important in visualizing how a gyro works. The bottom
axis is held stationary but can pivot in all directions.

When a tilting force is applied to the top axis, point A is sent in an upward
direction and C goes in a downward direction. FIG 1. Since this gyro is
rotating in a clockwise direction, point A will be where point B was when the
gyro has rotated 90 degrees. The same goes for point C and D. Point A is still
traveling in the upward direction when it is at the 90 degrees position in FIG
2, and point C will be traveling in the downward direction. The combined motion
of A and C cause the axis to rotate in the "precession plane" to the right FIG
2. This is called precession. A gyro's axis will move at a right angle to a
rotating motion. In this case to the right. If the gyro were rotating
counterclockwise, the axis would move in the precession plane to the left. If
in the clockwise example the tilting force was a pull instead of a push, the
precession would be to the left.

When the gyro has rotated another 90 degrees FIG 3, point C is where point A
was when the tilting force was first applied. The downward motion of point C is
now countered by the tilting force and the axis does not rotate in the "tilting
force" plane. The more the tilting force pushes the axis, the more the rim on
the other side pushes the axis back when the rim revolves around 180 degrees.

Actually, the axis will rotate in the tilting force plane in this example. The
axis will rotate because some of the energy in the upward and downward motion
of A and C is used up in causing the axis to rotate in the precession plane.
Then when points A and C finally make it around to the opposite sides, the
tilting force ( being constant) is more than the upward and downward counter
acting forces.

The property of precession of a gyroscope is used to keep monorail trains
straight up and down as it turns corners. A hydraulic cylinder pushes or pulls,
as needed, on one axis of a heavy gyro.

Sometimes precession is unwanted so two counter rotating gyros on the same axis
are used. Also a gimbal can be used.
THE GIMBALED GYROSCOPE
The property of Precession represents a natural movement for rotating bodies,
where the rotating body doesn’t have a confined axis in any plane. A more
interesting example of gyroscopic effect is when the axis is confined in one
plane by a gimbal. Gyroscopes, when gimbaled, only resist a tilting change in
their axis. The axis does move a certain amount with a given force.

A quick explanation of how a gimbaled gyro functions

Figure 4 shows a simplified gyro that is gimbaled in a plane perpendicular to
the tilting force. As the rim rotates through the gimbaled plane all the energy
transferred to the rim by the tilting force is mechanically stopped. The rim
then rotates back into the tilting force plane where it will be accelerated
once more. Each time the rim is accelerated the axis moves in an arc in the
tilting force plane. There is no change in the RPM of the rim around the axis.
The gyro is a device that causes a smooth transition of momentum from one plane
to another plane, where the two planes intersect along the axis.

A more detailed explanation of how a gimbaled gyro functions

Here I attempt to show how much the axis will rotate around a gimbaled axis.
That is to say, how fast it rotates in the direction of a tilting force.

In figure 4, the precession plane in the gimbaled example functions differently
than in the above example of figures 1-3, and I have renamed it "stop the
tilting force plane". The point masses at the rim are the only mass of the gyro
system that is considered. The mass and gyroscope effect of the axis is
ignored.

At first consider only ˝ of the rim, the left half. The point masses inside
the "stop the tilting force plane" share half their mass on either side of the
plane, and add their combined, 1/4kg, mass to point mass A of 1/2kg. So then
the total mass on the left side is ˝ the total mass of all 4 point masses, or
1kg. The tilting force will change the position of point mass B and D very
little and change the position of point mass A the most. So we must use the
average distance from the axis of all the mass on the left-hand side.
The mass on the left side is 1kg. The average distance the mass is from the
"stop the tilting force" plane is 1/2 meter. Figure 5 shows a profile of the
average mass in the tilting plane and the average distance from the axis that
the mass is situated. We are concerned at how far the mass at the average
distance will rotate within the tilting plane when a given force is applied to
the axis in the direction indicated.

Point mass A is rotating at 5 revolutions per second. This means that it is
exposed to the tilting force for only .1 seconds. The tilting force of 1
Newton, if applied for .1 second, will cause the mass at the average distance
to move .005 meter in an arc, in the tilting force plane. Since the length of
the axis is twice as long as the average distance of the rim’s mass, the axis
will move .01 meter in an arc. At the end of .1 second the point mass will be
in the "stop the tilting force plane" and all the energy transferred to point
mass A is lost in the physical restraint of the gimbal bearings.

The same thing happens when point mass A is on the right side of figure 4. Only
now, the tilting force will move point mass A down, and the axis will advance
another .01meter. .01 meter every .1 second is not the whole story because the
mass on the right side of the gyro hasn’t been considered. The right side has
the same mass as the left and has the same effect on the axis as the left side
does. So the axis will advance half as much, half of .01 meter, or .005meters.
Both halves of the rim mass will pass through the stop the tilting force plane
10 times in one second. Each time a half of the rim passes though the "stop the
tilting force plane", it losses all its momentum that was added by the tilting
force. The mass has to undergo acceleration again so we continually calculate
the effect that 1 Newton has for .1 second on the rim mass at the average
distance, 10 times a second. So then; at the point that the 1 Newton force is
applied, the axis will move 5cm per second along an arc. The gyro will rotate
at .48 RPM within the tilting force plane.

What considerations does the rim speed have on the distance
that the axis will rotate along an arc in the tilting force plane?

The gyro will rotate in the tilting force plane, half as fast if the rim speed
is doubled.

What happens when the mass of the rim is doubled?

The gyro will rotate in the tilting force plane, half as fast if the rim mass
is doubled

How does the rim diameter effect rotation in the tilting force
plane?

The gyro will rotate in the tilting force plane, half as fast if the rim
diameter is doubled

The Math of a gimbaled gyro

1 Newton = 1kilogram 1 meter sec.2

F=ma

d=1/2 X (a X t2
)

1 Newton acting on 1kg will accelerate the mass at a rate of 1 meter sec^2

the time that ˝ the mass of the rim is exposed to the tilting force at 5
revolutions a second is 10 times a second or 1/10; .1 sec

The axis is twice as long as the distance from the average distance that the
rim mass is calculated from .005 X 2 = .01 meters

Now consider the other side of the gyro as acted on by the same 1 Newton
force.
.01m / 2 = .005

The force will have ten times a second to accelerate the rim mass from a
relative velocity of 0m /sec.
10 X .005m = .05m; or 5 centimeters

Years ago there was a news story about a man that used a gyro to produce more
energy than was needed to keep the gyro spinning. He used a surplus ship's
directional gyro. I think what he did was use the property of precession to run
a generator.

If left undisturbed, a gyro on the surface of the Earth would turn 360 degrees
once every 24 hours. The top of the gyro would normally go westward. But if the
top axis were held so that it could not rotate from east to west, due to
precession, the gyro will rotate in the north and south direction depending on
the direction the rim is rotating. The gyro would turn due to precession until
it reaches 90 degrees with it's axis pointing north and south. Then it would be
in the same plane as the rotation of the Earth and gyroscopic precession would
stop. To get the gyro out of the Earth's rotational plain a small force could
be applied to the gyro axis and precession would put the axis back in the
original position. The 90 degree precession rotation would be much faster than
the once per 24 hours opposing forces rotation, but some gearing would probably
still be needed to run a generator. The generator would be mechanically linked
to the precession back and forth motion in one direction only so it will turn
the same direction all the time. The amount of energy needed to keep the gyro's
rim spinning and the energy needed to turn the gimbals back 90 degrees would
determine the overall efficiency.

This is NOT a free energy thing. The energy comes from the rotation of the
Earth and therefore the Earth rotational speed is slowed as energy is tapped
from a gyro-generator type machine. If this method of generating energy is used
to a great extent, days and nights would become longer. If this should happen.
let me be the first credited to use the term "rotation pollution" or "motion
pollution".

Other experiments with a gyro

There might be a way to accelerate the rotational speed of the rim of a gyro by
using a short duration tilting force on the axis. The force's duration would be
for much less then the length of time that is required for the rim to rotate 90
degrees. When the rim has rotated 90 degrees from the time the tilting force
was first applied, The tilting force would be purposely reversed. The direction
that the rim is rotating and the direction the rim would have moved due to
precession are now close to the same. The two motions might combine and result
in an increase in the rotational speed of the rim. T